Effects on Time-lapse Seismic
of a Hard Rock Layer beneath
a Compacting Reservoir
Pamela Tempone
Supervision: Martin Landrø & Erling Fjær
Problem Statement
Vertical Displacement [m]
Production
Reservoir
ΔP (ΔS, ΔV, Δφ,
Δρ, etc.)
Subsidence
Reservoir +
Surrounding
Δσ, Δε
Changes in
rock properties
Reservoir +
Surrounding
Depth [Km]
Compaction
Compacting
reservoir
ΔVp, Δ Vs, Δρ
Time-shift in
4D seismic survey
Distance [m]
4D Time-shift Prediction Method
1. Geomechanical
modeling
∙
Geertsma’s analytical model
2. Rock-physical modeling
∙
Dilation parameter
3. Seismic modeling
∙
Ray Tracing
ΔP
Geomechanical
modeling
σ,ε
Rock-physical
modeling
Vp, Vs, ρ
Synthetic seismic
modeling
4D Seismic Data vs Synthetic
Shearwater field (Staples et al, 2007)
Objective
• Cause: hard rock layer
beneath the
compacting reservoir
• Tool for capturing the
strong time-shifts in the
underburden
• Extension to
Geertsma’s analytical
solution
Shearwater field
(Staples et al, 2007)
Method
• Analytical solution:
superposition of 3 linear
systems;
• Additivity property of the
resultant system;
• Model assumption:
–
–
–
–
–
Zero stress at free surface;
Zero displacement at z=K;
Linear elastic medium;
Homogeneous medium;
Uniform deformation
properties;
Displacement due to a Nucleus
Underburden
System 1+2 is equivalent
to Geertsma’s solution
=
Nucleus of strain
2D model
Compacting reservoir
Velocity model
Additivity property of the
analytical solution
Displacement Fields
System 1+2
Geertsma’s model
System 3
Effect of the rigid layer
Displacement – Rigid Layer
Resultant system
Geertsma + Hard Rock Layer
Vertical displacement
Strain Field
Numerical solution
for the strain:
1  ui u j
 ij  

2  x j xi



Focus on the vertical strain
Reservoir
Vertical Strain
System 1+2
Geertsma’s model
Resultant system 1+2+3
Geertsma + Hard Rock Layer
Velocity Changes:
Dilation Parameter
• Change in relative seismic travel
time for a single layer of thickness
z (Landrø 2004):
t z V


t
z
V
• Linear dependence of elastic wave
velocities on strain (Hatchell 2005).
V
 R   z
V
• Lateral velocity changes
Layer
Overburden
Dilation
Factor
4
Reservoir
3.4
Underburden
8.5
Hard rock layer
10
Changes in P-wave velocity
System 1+2
Geertsma’s model
Horizontal position [m]
Resultant system 1+2+3
Geertsma + Hard Rock Layer
Horizontal position [m]
Synthetic Seismic Modeling
• Assuming reflector at
each discretization point
• Zero-offset TWT-shift is
computed as follows:
n
zi
TWT   1  R    zi 
Vpi
1
Hard Rock Layer
Geertsma’s
model
Time-shifts Synthetic
System 1+2 –
Geertsma’s model
Horizontal position [m]
Resultant system 1+2+3 –
Geertsma + Hard Rock Layer
Horizontal position [m]
Synthetics vs Real Data
Semi-analytical models:
Shearwater field
• Geertsma’s solution
(Staples et al, 2007)
(Green)
• Extension to
Geertsma’s solution
(Blu)
Time-shift
Discussions
•
•
•
•
Linear elastic medium
Homogeneous medium
Uniform deformation properties
Horizontal layer
• Horizontal displacement
• R factor has limitations
• No layer in the overburden
• Information from amplitude
Geomechanics
Rock physics
Syntetic Seismic
Conclusions I
Rigid layer causes:
•
An increase of the subsidence
•
An increase in the stretching between the bottom
reservoir and the rigid layer
•
A decrease in time-shift under the reservoir
Geertsma’s solution does not capture the strain field due to the stiff
layer in the underburden.
The increase of the time-shift along the overburden can be captured
manipulating the R factor.
Conclusions II
The extension to Geertsma’s model is:
• A tool for improving seismic time-lapse time-shift
interpretation
• A key for interpreting the sudden time-shift
reduction in the underburden
• Narrowing the gap between real data and
synthetic modeling
Future work
• Geomechanics:
– Extension to dipping reservoir and dipping rigid layer
– Analytical methods vs Finite Element Method (FEM)
• Synthetic seismic: FD modeling (TIGER)
• Analysis of a real data set (Field in North
Sea)
Acknowledgments
PETROMAX